By combining density functional theory(DFT)and impurity solver techniques realized by recently developed hierarchical equations of motion(HEOM)approach,we present a comprehensive picture of the Kondo effect in the dehydrogenated cobalt phthalocyanine molecule(d-CoPc)adsorbed on the Au(111)surface.We carryout ab initio simulations on the level of the GGA+U with the vdW corrections to obtain the proper adsorption geometry and correlated electronic structure.We find that the magnetic impurity singly occupied dz 2 orbital shows strong correlations which give rise to the asymmetric Kondo resonance at the Fermi level as observed in STM experiments.After establishing a single Anderson impurity model(AIM)to extend DFT calculations of the ground state,we employ HEOM approach to describe the Kondo resonance and Fermi-liquid characteristics.We show that the combined DFT+HEOM approach is suitable for the study of the Kondo resonance in the d-CoPc/Au(111)adsorption system,giving the corresponding spectral function and Fano features in the conductance-voltage.Our calculations yield the characteristic energy scale-the Kondo temperature(TK)and the differential conductance dI/dV spectra for the system in good agreement with experiments.The correct universal scaling behavior is also exhibited in good agreement with NRG methods.